Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
8,116 documents
The document collects suggested references for learning exotic option pricing and implementing pricing methods. The original question concerns volatility and variance swaps, jump diffusion, and explicit or implicit finite-difference methods, with particular…
The document discusses the inputs needed to price an FX option with a Black-Scholes style model when the trader has LIBOR quotes and historical exchange rates. One response suggests using the LIBOR rate nearest the option’s expiry, converting it to a…
The document explains how to estimate option Vega by bumping volatility and repricing, with examples involving multi-leg baskets and calendar spreads. Vega is a local sensitivity, so a one percentage point volatility move is a finite shock rather than a…
The document considers whether ordinary delta replication can hedge a quanto option, whose payoff is domestic-currency-denominated despite exposure to a foreign asset. The answer explains that holding delta in the foreign stock and borrowing in domestic cash…
The document examines whether a volatility surface for an inverse FX quote can be obtained by reversing call and put conventions around the at-the-money level. Its central explanation is that option delta depends on the currency used to measure the hedge. A…
The document asks how to approximate a down-and-out call price when the underlying follows the Heston stochastic-volatility model. It states the option payoff with a barrier condition, contrasts the problem with a Black–Scholes closed-form expression, and…
The document discusses using importance sampling to estimate prices for far out-of-the-money barrier options under local volatility. It describes changing the distribution of simulated inputs from the original density to a shifted normal density, then…
The document explains how the time increment in a simulated Heston model relates to the number of steps per year: once the time unit is fixed, choosing one determines the other. Its main example is the Euler–Maruyama discretization of the stock and variance…
The document asks how replication should be understood for an American option in a pricing model under a risk-neutral measure. A self-financing portfolio with an adapted strategy has a martingale value process, while an American option’s payoff process…
The document explains how to represent dual-curve pricing for caps and caplets in QuantLib Python. The curve handle supplied to the pricing engine is used to discount cash flows, while the curve associated with the Ibor index supplies forward rates.…
The document outlines a validation approach for a finite-difference implementation of the Libor Market Model. It recommends comparing European swaption prices across at-the-money and in-the-money or out-of-the-money strikes with prices from a zero-shift SABR…
The discussion examines when at-the-money (ATM) implied volatility can approximate the risk-neutral expectation of average integrated variance. For very short maturities, it motivates the approximation by noting that instantaneous volatility near the start…
The discussion asks whether implied volatility (IV) produces better option prices than historical volatility (HV), noting that the common forward-looking argument for IV is not enough by itself to establish better pricing performance. It cites an experiment…
The Longstaff–Schwartz method prices American options by simulating possible asset paths and using regression to estimate continuation values. The discussion notes that simulation can accommodate options whose value depends on multiple factors, so the method…
The document explains how an out-of-the-money put affects variance-covariance Value at Risk for a portfolio of stocks, bonds, an ETF, and an option. The method begins with market-factor volatilities and correlations, then combines factor sensitivities with…
The document asks whether the profit or loss of a Black-Scholes delta-hedged option depends only on realized volatility at expiry or also on its path. It references a hedge-error expression involving gamma exposure and the difference between implied variance…
The document examines a density that appears when expressing forward implied variance as an average of local variance. It derives the weighting from the risk-neutral distribution of the underlying and a factor involving spot squared and Black-Scholes gamma.…
The question examines the interest term in a derivation of the value change for a call option hedged by shorting delta shares. The reader reasons that buying the call requires borrowing its price, while short-sale proceeds from the shares are lent, implying…
The document clarifies that an option-adjusted spread is not a return that a hedge will realize on every interest-rate path. OAS is found by projecting an MBS’s cash flows across modeled rate paths, discounting them with the yield curve plus a spread, and…
The document compares two ways to obtain future distributions and price claims from an Itô process. A Fokker–Planck equation evolves the probability density through a deterministic partial differential equation, while Monte Carlo estimates outcomes from…
The document distinguishes several USD interest-rate curves that may appear in equity option pricing. A discount curve supplies discount factors for cash flows, but its name alone does not specify the benchmark or collateral convention used to construct it.…
The document surveys ways to obtain long-history intraday data for S&P 500 instruments, including index or ETF prices, futures, and options. The responses describe commercial vendors, exchange data shops, academic databases, and hosted research platforms.…
The document clarifies that normal and lognormal implied volatility refer to different option pricing conventions, not necessarily to the distribution assumed for the underlying in the SABR model. A normal implied volatility is the value used with Bachelier…
The document explains why a Double Heston model uses two stochastic variance processes. A second factor adds flexibility to the relationship between asset returns and volatility, allowing that correlation to change as the factors’ relative contributions…